Kinematics of mobile robots to complete a series of tasks

In the PDF, there are a number of tasks that need to be completed; the maximum time may take an hour.

4. Tasks

3.1. Simplified model of a car robot

• Prove the dependence between the steering angle of the virtual wheel and the angles of the front wheels.

3.2. Position determination from the kinematic model

• For a differential robot: derive the dependencies Δx, Δy, Δω at constant wheel speeds.

• For a car robot: similarly, at constant speed and steering angle.

3.3. Kinematics of bicycles and tricycles

• Compare the kinematics with Ackermann and analyze the influence of the instantaneous center of rotation (ICC).

3.4. Inverse kinematics

• Derive formulas for calculating control parameters (wheel speeds or speed and steering angle) along a given trajectory.

3.5. Kinematic simulation

• Using the simulator, perform the movement of the robot from the initial to the target pose in scenes 1–4 (Ackermann) and scenes 3–4 (differential robot).

• Using trial and error is prohibited — only calculations based on inverse kinematics.

• Errors: ±0.5 sq in coordinates, ±2° in orientation.

• Take screenshots of the final positions with a visible command list and log.